Sheet dispensers are often employed to dispense sheet products wound on a roll, such as paper towels and tissue, in common areas such as public washrooms. The cost of such dispensers is relatively high, and often these dispensers are provided at a discounted rate. Unless specifically provided for, a given dispenser may be suitable for many different varieties of sheet products, even those produced by different manufacturers. Under these conditions, the risk exists that the products offered in a dispenser may be those of a competitor. Separate from this commercial risk is the risk that products not designed specifically for a dispenser may impair operation of the dispenser. Therefore, “captive” systems of cooperating dispensers and sheet product rolls have been developed. Such captive systems accept specific types of sheet product rolls. One type of captive system involves a specially shaped end cap which fits into the core of the roll and also interacts in a complementary way with the roll supports inside the dispenser. Without the appropriate end cap, a roll cannot be inserted or dispenser does not function correctly.